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Fudgin [204]
3 years ago
10

Can you name the trigonometric expression that is equivalent to the following expression 1/secant of x?

Mathematics
1 answer:
Arlecino [84]3 years ago
8 0
The answer to your question is:  Yes, I can.


You haven't asked for the trigonometric expression, but here it is anyway:

The  <u>cosine</u>  function is the reciprocal of the secant function.
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Which polynomial function has a leading coefficient of 1 and roots (7 i) and (5 – i) with multiplicity 1? f(x) = (x 7)(x – i)(x
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It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.

The simplest polynomial with these characteristics would be

f(x) = (x - (7 + i)) (x - (5 - i))

but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with

f(x) = (x - (7 + i)) (x - (7 - i)) (x - (5 - i)) (x - (5 + i))

which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:

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